\subsection{Audio Effects}
When hearing the term \textit{sound effects}, many associate it with the act of creating/manipulating sounds for movies, e.g. making Foley sounds such as gunshots or explosions. However, it should not be confused with \textit{audio effects}, which is about changing a piece of audio using signal processing. This project is solely about the latter, and the chosen effects will be described in the following sections.

\subsubsection{Wah-wah Effect}
The 'wah-wah pedal' is a physical device with which it is possible to create the unique 'wah-wah effect'. Firstly, an acoustic signal is passed as input and its peak frequency is shifted up and down in the frequency spectrum \cite{filters4}. The magnitude of the shift is dependent on the pressure applied upon the foot pedal, as seen in figure \ref{fig:wahpic}. In simple terms, the wah effect is a low-pass or band-pass filter that allows the user to manually sweep the peak frequency up and down. Its most iconic characteristic can be heard when using an electric guitar, as made popular by Jimi Hendrix.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{images/TheoryDesign/wahpic}
\caption{The effect of a wah-wah pedal - applying pressure on the pedal affects the peak frequency of the input \cite{wahpic}.}
\label{fig:wahpic}
\end{figure}

\subsubsection{Flanger}
	The concept of flanging is having two signals playing in unison and then slowing one of them down slightly, causing a delay. After a fixed time, the two signals switch so the other one is playing slowly. Eventually they will momentarily play in unison again, and then the second signal will become the delayed signal for a certain time \cite{flanger}. 

\subsubsection{Chorus}
	The Chorus effect takes a single input, e.g. a voice, and makes it sound like there are multiple instances of the same voice singing a little differently. The chorus effect is rather similar to the flanger effect in that they both change the unison between signals \cite{chorus}. The difference comes in that chorus takes multiple samples of the same input and delays them differently to each other before collecting them once more.

\subsubsection{Phaser}
	A phaser effect have almost the same way of working as a flanger in the way that they both create delays over two unison signals. But where the flanger uses evenly spaced notches and peaks, the phaser uses a series of all-pass filters to do the same delay, which in turn creates notches and peaks that are spaced after the all-pass filter variables. Controlling the all-pass filters with an LFO (Low Frequency Oscillator) can give a 'swooshing' effect often associated with the phaser \cite{phasor}.

\subsubsection{Echo}
Delays and echoes are essentially the same when talking about audio. A delay implies that a signal is recorded and then played back after some period of time. An echo does the same, but often this is done repeatedly with attenuated volume and/or quality for each step to simulate the effect of a decaying echo in e.g. inside a cave.

In other words, an echo is a copy of the original audio signal that is delayed by a fixed amount in time and added to the signal \cite{delay_website}.

The key parameter here is the delay time; how long should the input be recorded before playing it. Other parameters are amplification of the repeated signal and whether it should use feedback of feedforward. Figure \ref{fig:delay} shows the echo effect, created by using feedforward.

The input enters from the left. The delayed version is then obtained by tapping it at the junction that is indicated by the small dot and goes to the box labelled with the delayed $\tau$. The addition of the signal to the delayed version of itself is shown in the conjugation with the summation symbol $\sum$ \cite{DSPPrimer}.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.3\textwidth]{images/TheoryDesign/delay_simple}
\caption{A simple feedforward delay \cite{DSPPrimer}.}
\label{fig:delay}
\end{figure}

\subsubsection{Vibrato and Tremolo}
Vibrato and tremolo are two very similar sound concepts and are often mixed up, an example being the tremolo controller on the famous Fender Stratocaster guitar actually being a vibrato controller. Vibrato can be defined as the rapid fluctuation of pitch in an audio signal, while tremolo can be defined as the fluctuation in volume or amplitude \cite{tremolo}. 

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{images/TheoryDesign/Vibrato_and_tremolo_graph}
\caption{A spectrum analysis comparison between vibrato and tremolo \ref{fig:vibrato&tremolo}.}
\label{fig:vibrato&tremolo}
\end{figure}

\subsubsection{Distortion}
The definition of distortion is the alteration of the original shape of something, such as in this case a wave. Normally distortion is something you want to avoid as much as possible to keep a sound as clean as possible, but in some cases it is desired, for example when using it as an effect when playing an electric guitar. Distortion refers to any modification or addition to a signal by any form of equipment \cite{audiodictionary} but in the context of effects, distortion is often associable with \textit{clipping}. Clipping is a non-linear effect which produces frequencies which are not originally found in the audio signal. There are two different types of clipping;

Soft clipping, which is an effect that gradually flattens the peaks of a signal; and hard clipping, which is an effect that simply cuts off the peaks of the signal, resulting in abrupt waves which are completely flat at their peak. Soft clipping suppresses the higher odd harmonics while the hard clipping emphasizes odd harmonics and results in a harsh sounding signal \cite{ElectronicsForGuitarists}.

The difference between the two clipping methods can be seen on figure \ref{fig:distortion}.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{images/TheoryDesign/distortion.png}
\caption{An original signal and the output of soft and hard clipping \cite{distortion}.}
\label{fig:distortion}
\end{figure}
